Optimal design method of separable‐denominator two‐dimensional digital filters based on a genetic algorithm

This paper proposes the optimal design for the separable‐denominator two‐dimensional digital filter, using the genetic algorithm (GA). the design proposed is for the specification in the frequency domain. the simple GA, which is the most basic among GA, is used in the proposed optimal design. the parameters of the transfer function of the separable‐denominator twodimensional digital filter are encoded into bit sequences, and then GA is applied to design the filter. By the use of the separable‐denominator transfer function, the stability of the filter is completely guaranteed. The approximation error of the proposed method is compared to that of the conventional method through design examples. the convergence of GA is discussed. It is shown that the proposed optimal design can easily cope with the modification of the design specification of the two‐dimensional digital filter. It is shown also that the filter can be designed using the maximum error or the absolute error sum as the error evaluation function in addition to the mean‐square error.